Question: 4. A linear cyclic code (n,k) has code length n=7 and generator polynomial g(X)=1+X2+X3+X4. (a) Find the code rate, the generator and parity check matrices

4. A linear cyclic code (n,k) has code length n=7 and

4. A linear cyclic code (n,k) has code length n=7 and generator polynomial g(X)=1+X2+X3+X4. (a) Find the code rate, the generator and parity check matrices of the code in systematic form, and its Hamming distance. (b) If all the information symbols are ' 1 's, what is the corresponding code vector? (c) Find the syndrome corresponding to an error in the first information symbol, and show that the code is capable of correcting this error

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock blur-text-image

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Databases Questions!

help!!!! Q6 1-A linear cyclic code (n, k) has code length n = 7 and generator polynomial g(x) = 1 + x + x + x (a) Find the code rate, the generator and parity check matrices of the code in systematic...

1- A linear cyclic code ( n , k ) has code length n = 7 and generator polynomial g ( X ) = 1 + X 2 + X 3 + X 4 (a) Find the code rate, the generator and parity check matrices of the code in...

Q6 1-A linear cyclic code (n, k) has code length n = 7 and generator polynomial g(x) = 1 + x + x + x (a) Find the code rate, the generator and parity check matrices of the code in systemat form, and...

A binary linear cyclic code Ccyc(n, k) has code length n= 7 and generator poly- nomial g(x) = 1 + X + X + X4. (a) Find the code rate, the generator and parity check matrices of the code in systematic...

Q 4 ) A linear cyclic code ( n , k ) has code length n = 7 and generator polynomial g ( x ) = 1 + x 2 + x 3 + x 4 ( a ) Find the code rate, the generator and parity check matrices of the code in...

1. (a) What is meant by a cyclic error-control code? Explain your answer by suitable examples (at least 2). (b) Can cyclic codes be non-linear? Explain your answer by suitable examples (at least 2)....

Consider a ( 7 , 4 ) linear block code defined by the generator matrix G: G = 1 0 0 0 1 1 0 0 1 0 0 0 1 1 0 0 1 0 1 1 1 0 0 0 1 1 0 1 . ( a ) Find the parity check matrix H of the code in systematic...

Q10 A linear cyclic block code (n, k) has code length of n = 14 and has generator polynomial g(x) = 1 + x + x (a) Determine the number of information and parity check bits in each code vector. (b)...

Probability and Statistics - Problem Set c Keith M. Chugg October 2, 2015 1 Preliminaries, Combinatorics, Set Probability 1.1. A number of bats are in a cave. 2 bats can see out of their left eye. 3...

s1 educated (SSE) student for every three public school educated (PSE) students. Reasoning that students are not very dissimilar from threads, he suggests the following entry and exit routines be...

Water is boiling at 1 atm pressure in a stainless steel pan on an electric range. It is observed that 2 kg of liquid water evaporates in 30 min. The rate of heat transfer to the water is (a) 2.51 kW...

Consider the following assets: E(r) Asset A Market portfolio, M Risk-free asset SD Beta 30% 1 8% 15% 2% Currently all your client's funds are invested in stock A. a) Currently, your portfolio...

Starbucks recently reported net income of $ 4 , 5 1 8 . 3 million. Its stockholders equity was $ 5 , 4 5 0 . 1 million and $ 1 , 1 6 9 . 5 million at the beginning and end of the fiscal year,...

CT Corp Comprehensive Question Canadian Tire Corporation, Limited (Canadian Tire) is a family of companies that includes a retail segment and a financial services division, among others. The retail...

Family coordination. Despite the eroding of the traditional family in many of the Soviet republics, there is evidence that family traditions and ties had survived despite Sovietization and...

branch ministries to which enterprises were directly subordinated, and which were responsible for translating directives of the functional committees into concrete operating decisions for the...

Self-governing coordination. The nominal character of cooperative enterprises was of self-governance, but only vestiges of a system of proposals or criticisms from below pertained in practice. It is...